Exact reformulation of the bosonic many-body problem in terms of stochastic wavefunctions : convergences issues

Iacopo Carusotto, Yvan Castin

Iacopo Carusotto, Yvan Castin

There exist methods to reformulate in an exact way the many-body problem of interacting bosons in terms of the stochastic evolution of single particle wave functions. For one such reformulation, the so-called simple Fock scheme, we present an elementary derivation, much simpler than the original one. Furthermore, we show that two other schemes, based on coherent states of the matter field rather than on Fock states, lead to an infinite statistical uncertainty in the continuous time limit. The simple Fock scheme is therefore, up to now, the only one that was proved to lead to a convergent Monte Carlo simulation scheme at all times.

Iacopo Carusotto, Yvan Castin

Recently, a new method was developed to reformulate in an exact way the N-body problem of interacting bosons in terms of the stochastic evolution of single particle wavefunctions, see I. Carusotto Y. Castin, and J. Dalibard, Phys. Rev. A 63, 023606 (2001) . The original derivation is however often considered as rather involved. For the specific scheme called `simple Fock scheme’ we present here a very elementary derivation of such an approach.

Y. Suzuki, Kálmán Varga

David M. Ceperley

Murat Çetinbaş, Joshua Wilkie

We show that any non-relativistic quantum N-body dynamics problem with pairwise interactions can be exactly reformulated in terms of N well behaved 1-body stochastic density equations. Specifically, the time evolving N-body density matrix is written as an average of tensor products of 1-body densities each of which obeys a stochastic evolution equation. Such decompositions can be constructed for any mixture of fermions and bosons. The evolution equations for the 1-body densities preserve norm, Hermiticity and positivity.